Evaluating efficiency of counties in providing diabetes preventive care using data envelopment analysis

Abstract

For patients with diabetes, annual preventive care is essential to reduce the risk of complications. Local healthcare resources affect the utilization of diabetes preventive care. Our objectives were to evaluate the relative efficiency of counties in providing diabetes preventive care and explore potential to improve efficiencies. The study setting is public and private healthcare providers in US counties with available data. County-level demographics were extracted from the Area Health Resources File using data from 2010 to 2013, and individual-level information of diabetes preventive service use was obtained from the 2010 Behavioral Risk Factor Surveillance System. 1112 US counties were analyzed. Cluster analysis was used to place counties into three similar groups in terms of economic wellbeing and population characteristics. Group 1 consisted of metropolitan counties with prosperous or comfortable economic levels. Group 2 mostly consisted of non-metropolitan areas between distress and mid-tier levels, while Group 3 were mostly prosperous or comfortable counties in metropolitan areas. We used data enveopement analysis to assess efficiencies within each group. The majority of counties had modest efficiency in providing diabetes preventive care; 36 counties (57.1%), 345 counties (61.1%), and 263 counties (54.3%) were inefficient (efficiency scores < 1) in Group 1, Group 2, and Group 3, respectively. For inefficient counties, foot and eye exams were often identified as sources of inefficiency. Available health professionals in some counties were not fully utilized to provide diabetes preventive care. Identifying benchmarking targets from counties with similar resources can help counties and policy makers develop actionable strategies to improve performance.

Appendix A

Data envelopment analysis (DEA) provides a measure of efficiency for each decision-making unit (DMU) among a set of peer groups by comparing inputs consumed to produce outputs based on linear programming (LP). DMUs are indexed by $j = 1, 2, \ldots ,j_{0} , \ldots ,N$. Inputs of DMU_j are denoted by {$x_{ij} ;i = 1, 2, \ldots ,m^{\prime}, m^{\prime} + 1, \ldots ,M;j = 1, 2, \ldots N)$, where $i = 1, 2, \ldots ,m^{\prime}$ is discretionary input variables and $i = m^{\prime} + 1, m^{\prime} + 2, \ldots M$ is non-discretionary input variables. Outputs of DMU_j are denoted by {$y_{rj} ;r = 1, 2, \ldots ,R;j = 1, 2, \ldots N)$. The dual form of output-oriented Banker, Charnes, and Cooper (BCC) model that assumes variable returns-to-scale can be formulated as follows:

$$ \begin{array}{*{20}l} {{\text{Max}}} \hfill & {\theta_{0} + \varepsilon \left(\mathop \sum \limits_{i = 1}^{{m^{\prime}}} s_{i}^{ - } + \mathop \sum \limits_{r = 1}^{R} s_{r}^{ + } \right)} \hfill \\ {{\text{subject}}\;{\text{to}}} \hfill & {\mathop \sum \limits_{j = 1}^{N} \lambda_{j} Y_{rj} - s_{r}^{ + } = \theta_{0} Y_{{rj_{0} }} \left( {r = 1, 2, \ldots ,R} \right)} \hfill \\ {} \hfill & {\mathop \sum \limits_{j = 1}^{N} \lambda_{j} X_{ij} + s_{i}^{ - } = X_{{ij_{0} }} \left( {i = 1, 2, \ldots ,M} \right)} \hfill \\ {} \hfill & {\mathop \sum \limits_{j = 1}^{N} \lambda_{j} = 1} \hfill \\ {} \hfill & {\quad \lambda_{j} \ge 0, s_{i}^{ - } \ge 0 , \;s_{r}^{ + } \ge 0 \left( {i = 1, 2, \ldots , m^{\prime};\, j = 1, 2, \ldots N ;\,r = 1, 2,..R} \right)} \hfill \\ \end{array} $$

where the scalar variable $\theta_{0}$ represents the efficiency score of the DMU being evaluated (DMU₀), s⁺ and s⁻ are slack variables, and $\varepsilon > 0$ is a small non-Archimedean number. Positive slacks may indicate the possible presence of alternate optima and inefficiency. The term with a non-Archimedean number in the objective function addresses this problem by maximizing the slacks without altering the $\theta_{0}$ value. A DMU_j is efficient if and only if $\theta_{j} = 1$ and all slacks are zero.

For this study, we used four inputs and four outputs. Inputs are (1) the number of individuals with diabetes, (2) the number of primary care physicians, (3) the number of APNs, and (4) the number of optometrists and ophthalmologists in each county. The number of individuals with diabetes is used as a nondiscretionary input variable. While this variable cannot be directly controlled by counties, it is important to include it in the DEA model because outputs are bound by the number of people who need the services. Outputs are (1) the number of patients who had eye exams, (2) the number of patients who had foot exams, (3) the number of patients who had annual doctor visits for diabetes, and (4) the number of patients who had 1 or more A1c test in each county. For an output-oriented DEA model, inefficient DMUs have an efficiency score of greater than 1, where ($1 - \theta_{j} )$ indicates the proportional increase applied to all outputs of the DMU_j to improve efficiency. To make the interpretation of the secondary analysis easier, we use the inverse of the efficiency score (i.e., DMU is inefficient if $\theta < 1$).